Sufficiency and statistical decision functions

Abstract

This paper contains an account, in abstract terms, of sufficiency and of its role in statistical decision problems. The study of sufficiency in abstract terms was initiated by Halmos and Savage [1], and the present paper, although self-contained, is to be regarded as a continuation of their work. The main objects of the paper are to show that the justification for the use of sufficient statistics in statistical methodology which is sketched in the final section of [1] is valid under certain quite general conditions, and to extend this justification to the case of sequential experiments. The paper falls into two parts of which the first (Sections 2-7) is mainly expository and provides an account of the theory of sufficiency in the nonsequential case. The second part (Sections 8-11) then extends the theory to sequential experiments.